Limits of expression with square root

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SUMMARY

The discussion focuses on the mathematical limits of the expression sqrt(A + Bt) as time (t) approaches zero and infinity, where A and B are constants. As t approaches zero, the expression simplifies to sqrt(A). Conversely, as t approaches infinity, provided that B is greater than zero, the expression behaves like sqrt(Bt) due to the dominance of the Bt term. The inquiry also considers the potential use of Taylor series expansion to analyze the limits without assumptions about the relative sizes of A and B.

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I am looking at the derivation for an expression that relates the concentration of an oxide to time. It appears that to do this, the author takes the limit of sqrt(A+Bt), where A and B are constants as t approaches zero and infinity. Is there an easy way to do this without making assumptions about the sizes of the terms (ex. Bt >> A)? Could I expand this as a Taylor series?
 
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Since the sqrt is continuous, when t->0 you are simply left with sqrt(A). As t->oo, as long as B >0, eventually Bt >> A, so it behaves like sqrt(Bt).
 

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